Enchine comes from the verb enchinar, which means to make something curl or to make one's skin tingle or get goosebumps. It's a vivid and somewhat unique verb that captures a physical reaction to intense feeling.
In the song, the singer describes the ideal lover as someone who can make her skin tingle with a kiss ("que en un beso intenso te enchine la piel"), highlighting a deep, physical connection and passion. It's a memorable way to express a powerful emotional and physical response.
Julión Álvarez spends most of this song simply handing out compliments. He greets her as princesa, tells her she looks beautiful even though it is not her birthday, and calls her level-headed, smart, kind and well brought up. By the time he decides she is toda una diosa, it sounds like a straightforward love letter.
Then the punchline arrives. Every menu is missing one dish, he says, and what she needs is someone who treats her well, who makes her skin tingle with a kiss, who would rearrange the stars into her face and name the brightest one after her. That someone, naturally, is him: without me you are almost complete. It is a norteño chat-up line delivered with a wink, and a nice place to pick up warm everyday Spanish like te digo la neta.